Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.Scanner;


public class A121div2 {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		long n2 = 2*n;
		boolean b = false;
		for (long i = 1; i*i + i < n2; i++) {
			long r = n2 - (i*i + i);
			long D = 1 + 4*r;
			long sd = (long)Math.sqrt(D);
			if(sd*sd == D) {
				long t = -1 + sd;
				if(t % 2 == 0) {
					b = true;
					break;
				}
			}
		}
		System.out.println(b ? "YES" : "NO");
	}

}